Overordnede kursusmål
The theory of optics is so rich and complex that many theoretical
formalisms have been formulated to describe, analyze, simulate and
quantify its physical properties. Among all these formalisms
phenomenological approaches like radiometry and radiative transfer,
originally stated in the context of astrophysics, are very
convenient and widely used to simulate light propagation and
light-matter interactions. Phenomenon like scattering of light by a
random media or rough surface are well explained by radiative
transfer theory, as well as macroscopic light-matter interactions
through the concept of bi-scattering-distribution-function (BSDF).
In this course, we will give significant theoretical and practical
insights of this theory, which is of particular importance of many
fields of science and engineering.
Læringsmål
En studerende, der fuldt ud har opfyldt kursets mål, vil kunne:
- • Analyze and characterize optical properties of materials
important for light transport
- • Model, derive, measure and efficiently utilize
bi-scattering-distribution-functions
- • Manipulate and solve the integral equations governing light
transport in both scalar and vector forms
- • Simulate and model light transport and light-matter
interactions for engineering and scientific applications from
optical engineering to astrophysics
- • Predict and solve the (multiple/single) scattering of light
by random scatterers, both in volume and surface
- • Derive mathematical and numerical models for light transport
modeling and simulation
- • Describe and interpret the principles of optical simulation
software and raytracing based algorithms
- • Conduct numerical simulations for solving complex light
transport and light matter interaction problems, without directly
solving PDEs like Maxwell’s or Wave equations
- • Derive analytical solutions of Maxwell’s equations
Kursusindhold
The course consists of four parts:
1. Review of theory of optics
2. Radiative transfer equation (RTE): theory and applications
3. Light scattering and bi-directional scattering functions
4. Numerical methods and algorithms for solving the RTE and
scattering problems
We will start from reviewing electromagnetic and wave approaches of
principles of optics, and related mathematical concepts. This part
will also review optical properties of materials; this will be
useful for the modelling and simulation of light transport
problems.
In a second part of the course, we will depart from Maxwell’s and
wave equations to derive the radiative transfer equation, which is
based on geometrical optics but can fully embrace waves optics
properties like polarization. In this part of the course, we will
also discuss integral equations, as the RTE is part of this class
of equations; other integral equations that will be discussed
include Kirchhoff and Stratton-Chu integrals.
Then equipped with the theoretical foundation of radiative transfer
and integral equations we will approach the problem of light
scattering and explain it through the RTE formalism. In this part,
we will also introduce the concept of
bi-scattering-distribution-function (BSDF). Polarization will be
also discussed in this section, and we will see how to include it
in a ray-based theory through Stokes formalism and vector integral
equations. Based on understanding of the theoretical aspects of
radiative transfer we will learn to solve integral equations with
raytracing and Monte Carlo methods, and present some commercial and
open source simulation packages based on these techniques.
Sidst opdateret
19. oktober, 2016
